For a "something for everyone" atmposphere I'd recommend looking at Royal Caribbean.. either Freedom or Liberty of the Seas.

These attract a broad demographic, and activities planned will span all age groups. Lots of families onboard, but they also attract young singles.

Second choice would be one of the Carnival Conquest Class ships... maybe Carnival's Freedom (silly, same name I know ) They're lively ships, and they do schedule some single activities to allow singles to meet others in a similar situation.